Abstract

The continuous spectrum is a unique representation of the linear viscoelastic behavior of a polymer that reveals aspects of its behavior that may not be obvious in plots of the storage and loss moduli. A spectrum can in principle be inferred from experimental data, but because data are always corrupted by random error, this is one of the several ill-posed problems that arise in rheology [Honerkamp, J., Rheol. Acta 28, 363–371 (1989) and Malkin, A. Ya., Rheol. Acta 29, 512–518 (1990)], and this throws into doubt the possibility of obtaining a unique relaxation spectrum. A number of methods have been proposed to overcome the ill-posedness of the problem to arrive at a unique continuous spectrum that is a characteristic of the material. Wider use of these methods has been limited by the fact that many of them are the work of mathematicians or physicists who use languages and symbols not readily intelligible to rheologists and that the codes required to implement them are not readily available. For these reasons, continuous spectra are rarely reported. We demonstrate and compare the use of one, well-established method as well two recent ones using both simulated and actual data and provide advice to polymer rheologists as to the feasibility of inferring a meaningful continuous spectrum from data. We also evaluate the method of Baumgaertel and Winter [J. Non-Newtonian Fluid Mech. 44, 15–36 (1992)] for obtaining a discrete spectrum that is useful for calculating material functions and for flow simulation. We recommend that reports of viscoelastic behavior include plots of this revealing material function.

Received 23 October 2013Revised 24 March 2014Accepted 25 March 2014Published online 23 April 2014

Acknowledgments:

The authors received helpful assistance from Professor K. S. Cho, Professor A. R. Davies, Professor J. Honerkamp, Professor F. J. Stadler, and Professor H. H. Winter as well as Dr. Si Wan (Michelle) Li and Gun Woo Park. The rock foundation upon which our work is built is the classic book by the late John Ferry (1980).